Continuum model of the simple dielectric fluid: consistency between density based and continuum mechanics methods

The basic continuum model for polar fluids is deceptively simple. free energy integral consists of four terms: coupling polarization to an external field, the electrostatic induced electric field interacting with itself and stored quadratic in polarization. A local function density accounts mechanical state fluid. Viewed as a non-equilibrium functional number polarization, minimization these two densities under constraints Maxwell equations should lead correct equilibrium state. alternative mechanics approach which degree freedom extended full deformation. We show that electromechanics method leads force balance equation consistent equation. procedure significantly more demanding. gain well defined pressure tensor derived from deformation total energy. This resolves issue uncertainty obtained integration density, conventional based thermomechanics. Our derivation on variational electrostatics developed by Ericksen (Arch. Rational Mech. Anal. {\bf 183} 299 (2007)).